OP said that there is a box on the application form that if checked, says that the applicant has read and agrees to the policies in the manual. That is where this policy of revoking the degree is located.
That is really not part of the contract between the student and the college. Just because an applicant has read the policies and agrees does not make it part of the contract unless there is specific language in the contract (or in the policy manual) that says it is part of the contract. I believe this is governed by the statutes of frauds.
I don't think checking a box on an application does it.To satisfy the requirements of a typical statute, the writing must identify the contracting parties, recite the subject matter of the contract such that it can reasonably be identified, and present the essential terms and conditions of the parties' agreement.
Next is the issue of estoppel both promissory and equitable. I'm still work on those.